WIAS Preprint No. 445, (1998)

Iterative procedure for multidimensional Euler equations


  • Dreyer, Wolfgang
  • Kunik, Matthias
  • Sabelfeld, Karl
  • Simonov, Nikolai
  • Wilmánski, Krzysztof

2010 Mathematics Subject Classification

  • 35L45 35L65 35L67 82B40 11K45


  • Initial value problems, hyperbolic systems of first order, conservation laws, shocks, kinetic theory, Monte Carlo methods


A numerical iterative scheme is suggested to solve the Euler equations in two and three dimensions. The step of the iteration procedure consists of integration over the velocity which is here carried out by three different approximate integration methods, and in particular, by a special Monte Carlo technique. Regarding the Monte Carlo integration, we suggest a dependent sampling technique which ensures that the statistical errors are quite small and uniform in space and time. Comparisons of the Monte Carlo calculations with the trapezoidal rule and a gaussian integration method show good agreement.

Appeared in

  • Monte Carlo Methods and Appl., 4 (1998), No. 3, pp. 253-271

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